ABSTRACT

Charging balls with a branching Markov diffusion.

Andreas Kyprianou, October 10, 2001

Consider a branching diffusion in which each individual moves as a Markov diffusion with corresponding operator L and branches at a (spatial) rate b into precisely two particles at each fission point. Suppose the process begins from an individual particle. Given any ball and starting position, does a criteria exist which will guarentee the ball is visited (or charged) infinitely often by the branching process with positive/zero probability. The answer is yes and the criteria concerns the the sign (+/-) of the minimum l such that there exist a positive harmonic function with respect to the operator (L+b-l). The number l is called the generalized principal eigenvalue. The theory is illustrated with a branching Brownian motion example.

This is joint work with Janos Englander (EURANDOM).

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Martijn Pistorius (pistorius@math.uu.nl)

Last Updated: October 1, 2001